Properties

Label 378.2.z.a.293.9
Level $378$
Weight $2$
Character 378.293
Analytic conductor $3.018$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(41,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([17, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.z (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 293.9
Character \(\chi\) \(=\) 378.293
Dual form 378.2.z.a.209.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.342020 + 0.939693i) q^{2} +(0.288948 + 1.70778i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.675752 + 3.83238i) q^{5} +(-1.70361 - 0.312573i) q^{6} +(-0.478059 - 2.60220i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.83302 + 0.986917i) q^{9} +O(q^{10})\) \(q+(-0.342020 + 0.939693i) q^{2} +(0.288948 + 1.70778i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.675752 + 3.83238i) q^{5} +(-1.70361 - 0.312573i) q^{6} +(-0.478059 - 2.60220i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.83302 + 0.986917i) q^{9} +(-3.37014 - 1.94575i) q^{10} +(-2.70819 + 0.477527i) q^{11} +(0.876392 - 1.49397i) q^{12} +(0.574003 + 1.57706i) q^{13} +(2.60878 + 0.440778i) q^{14} +(-6.74011 - 0.0466780i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.48502 + 4.30419i) q^{17} +(0.0415504 - 2.99971i) q^{18} +(6.24771 - 3.60712i) q^{19} +(2.98106 - 2.50141i) q^{20} +(4.30585 - 1.56832i) q^{21} +(0.477527 - 2.70819i) q^{22} +(3.43594 - 4.09479i) q^{23} +(1.10413 + 1.33451i) q^{24} +(-9.53201 - 3.46937i) q^{25} -1.67827 q^{26} +(-2.50403 - 4.55300i) q^{27} +(-1.30645 + 2.30069i) q^{28} +(-0.869378 + 2.38860i) q^{29} +(2.34912 - 6.31767i) q^{30} +(-5.22704 + 6.22935i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-1.59804 - 4.48701i) q^{33} +(-3.19468 - 3.80728i) q^{34} +(10.2957 - 0.0736588i) q^{35} +(2.80460 + 1.06501i) q^{36} +(-0.177172 + 0.306871i) q^{37} +(1.25274 + 7.10463i) q^{38} +(-2.52741 + 1.43596i) q^{39} +(1.33097 + 3.65681i) q^{40} +(3.97955 - 1.44844i) q^{41} +(0.00104912 + 4.58258i) q^{42} +(1.65693 + 9.39692i) q^{43} +(2.38154 + 1.37498i) q^{44} +(-1.86782 - 11.5241i) q^{45} +(2.67269 + 4.62923i) q^{46} +(-5.79089 + 4.85913i) q^{47} +(-1.63166 + 0.581111i) q^{48} +(-6.54292 + 2.48801i) q^{49} +(6.52028 - 7.77057i) q^{50} +(-8.06864 - 3.00019i) q^{51} +(0.574003 - 1.57706i) q^{52} -6.43428i q^{53} +(5.13485 - 0.795801i) q^{54} -10.7015i q^{55} +(-1.71511 - 2.01454i) q^{56} +(7.96542 + 9.62744i) q^{57} +(-1.94720 - 1.63390i) q^{58} +(-0.927668 + 5.26107i) q^{59} +(5.13322 + 4.36822i) q^{60} +(3.29907 + 3.93168i) q^{61} +(-4.06592 - 7.04237i) q^{62} +(3.92251 + 6.90028i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.43177 + 1.13409i) q^{65} +(4.76297 + 0.0329855i) q^{66} +(-1.47671 + 0.537479i) q^{67} +(4.67032 - 1.69986i) q^{68} +(7.98581 + 4.68464i) q^{69} +(-3.45211 + 9.69996i) q^{70} +(6.90603 + 3.98720i) q^{71} +(-1.96001 + 2.27120i) q^{72} +(-1.45847 + 0.842046i) q^{73} +(-0.227768 - 0.271443i) q^{74} +(3.17066 - 17.2810i) q^{75} +(-7.10463 - 1.25274i) q^{76} +(2.53730 + 6.81898i) q^{77} +(-0.484933 - 2.86612i) q^{78} +(15.6048 + 5.67967i) q^{79} -3.89150 q^{80} +(7.05199 - 5.59191i) q^{81} +4.23495i q^{82} +(3.91696 + 1.42566i) q^{83} +(-4.30657 - 1.56635i) q^{84} +(-14.8160 - 12.4321i) q^{85} +(-9.39692 - 1.65693i) q^{86} +(-4.33040 - 0.794527i) q^{87} +(-2.10660 + 1.76765i) q^{88} +(2.32657 + 4.02974i) q^{89} +(11.4680 + 2.18630i) q^{90} +(3.82942 - 2.24760i) q^{91} +(-5.26416 + 0.928214i) q^{92} +(-12.1487 - 7.12668i) q^{93} +(-2.58549 - 7.10357i) q^{94} +(9.60193 + 26.3811i) q^{95} +(0.0119949 - 1.73201i) q^{96} +(-8.44682 + 1.48940i) q^{97} +(-0.100156 - 6.99928i) q^{98} +(7.20107 - 4.02560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.342020 + 0.939693i −0.241845 + 0.664463i
\(3\) 0.288948 + 1.70778i 0.166824 + 0.985987i
\(4\) −0.766044 0.642788i −0.383022 0.321394i
\(5\) −0.675752 + 3.83238i −0.302205 + 1.71389i 0.334171 + 0.942512i \(0.391544\pi\)
−0.636376 + 0.771379i \(0.719567\pi\)
\(6\) −1.70361 0.312573i −0.695497 0.127607i
\(7\) −0.478059 2.60220i −0.180689 0.983540i
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) −2.83302 + 0.986917i −0.944340 + 0.328972i
\(10\) −3.37014 1.94575i −1.06573 0.615300i
\(11\) −2.70819 + 0.477527i −0.816550 + 0.143980i −0.566298 0.824201i \(-0.691625\pi\)
−0.250253 + 0.968181i \(0.580514\pi\)
\(12\) 0.876392 1.49397i 0.252993 0.431271i
\(13\) 0.574003 + 1.57706i 0.159200 + 0.437398i 0.993489 0.113930i \(-0.0363438\pi\)
−0.834289 + 0.551327i \(0.814122\pi\)
\(14\) 2.60878 + 0.440778i 0.697225 + 0.117803i
\(15\) −6.74011 0.0466780i −1.74029 0.0120522i
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −2.48502 + 4.30419i −0.602707 + 1.04392i 0.389703 + 0.920941i \(0.372578\pi\)
−0.992409 + 0.122978i \(0.960756\pi\)
\(18\) 0.0415504 2.99971i 0.00979353 0.707039i
\(19\) 6.24771 3.60712i 1.43332 0.827529i 0.435950 0.899971i \(-0.356412\pi\)
0.997373 + 0.0724417i \(0.0230791\pi\)
\(20\) 2.98106 2.50141i 0.666585 0.559332i
\(21\) 4.30585 1.56832i 0.939614 0.342235i
\(22\) 0.477527 2.70819i 0.101809 0.577388i
\(23\) 3.43594 4.09479i 0.716443 0.853823i −0.277837 0.960628i \(-0.589618\pi\)
0.994280 + 0.106805i \(0.0340620\pi\)
\(24\) 1.10413 + 1.33451i 0.225379 + 0.272405i
\(25\) −9.53201 3.46937i −1.90640 0.693874i
\(26\) −1.67827 −0.329136
\(27\) −2.50403 4.55300i −0.481901 0.876226i
\(28\) −1.30645 + 2.30069i −0.246896 + 0.434790i
\(29\) −0.869378 + 2.38860i −0.161439 + 0.443551i −0.993867 0.110583i \(-0.964728\pi\)
0.832427 + 0.554134i \(0.186951\pi\)
\(30\) 2.34912 6.31767i 0.428888 1.15344i
\(31\) −5.22704 + 6.22935i −0.938804 + 1.11882i 0.0539358 + 0.998544i \(0.482823\pi\)
−0.992740 + 0.120279i \(0.961621\pi\)
\(32\) −0.984808 0.173648i −0.174091 0.0306970i
\(33\) −1.59804 4.48701i −0.278182 0.781088i
\(34\) −3.19468 3.80728i −0.547884 0.652942i
\(35\) 10.2957 0.0736588i 1.74029 0.0124506i
\(36\) 2.80460 + 1.06501i 0.467433 + 0.177501i
\(37\) −0.177172 + 0.306871i −0.0291269 + 0.0504492i −0.880221 0.474563i \(-0.842606\pi\)
0.851095 + 0.525012i \(0.175939\pi\)
\(38\) 1.25274 + 7.10463i 0.203221 + 1.15252i
\(39\) −2.52741 + 1.43596i −0.404710 + 0.229937i
\(40\) 1.33097 + 3.65681i 0.210445 + 0.578193i
\(41\) 3.97955 1.44844i 0.621502 0.226208i −0.0120264 0.999928i \(-0.503828\pi\)
0.633528 + 0.773719i \(0.281606\pi\)
\(42\) 0.00104912 + 4.58258i 0.000161883 + 0.707107i
\(43\) 1.65693 + 9.39692i 0.252680 + 1.43302i 0.801959 + 0.597379i \(0.203791\pi\)
−0.549280 + 0.835638i \(0.685098\pi\)
\(44\) 2.38154 + 1.37498i 0.359031 + 0.207287i
\(45\) −1.86782 11.5241i −0.278439 1.71791i
\(46\) 2.67269 + 4.62923i 0.394066 + 0.682543i
\(47\) −5.79089 + 4.85913i −0.844687 + 0.708777i −0.958613 0.284712i \(-0.908102\pi\)
0.113926 + 0.993489i \(0.463657\pi\)
\(48\) −1.63166 + 0.581111i −0.235510 + 0.0838761i
\(49\) −6.54292 + 2.48801i −0.934703 + 0.355430i
\(50\) 6.52028 7.77057i 0.922107 1.09892i
\(51\) −8.06864 3.00019i −1.12984 0.420110i
\(52\) 0.574003 1.57706i 0.0795998 0.218699i
\(53\) 6.43428i 0.883817i −0.897060 0.441908i \(-0.854302\pi\)
0.897060 0.441908i \(-0.145698\pi\)
\(54\) 5.13485 0.795801i 0.698765 0.108295i
\(55\) 10.7015i 1.44299i
\(56\) −1.71511 2.01454i −0.229192 0.269205i
\(57\) 7.96542 + 9.62744i 1.05505 + 1.27519i
\(58\) −1.94720 1.63390i −0.255680 0.214541i
\(59\) −0.927668 + 5.26107i −0.120772 + 0.684932i 0.862957 + 0.505277i \(0.168610\pi\)
−0.983730 + 0.179656i \(0.942502\pi\)
\(60\) 5.13322 + 4.36822i 0.662696 + 0.563934i
\(61\) 3.29907 + 3.93168i 0.422402 + 0.503400i 0.934714 0.355400i \(-0.115655\pi\)
−0.512312 + 0.858799i \(0.671211\pi\)
\(62\) −4.06592 7.04237i −0.516372 0.894382i
\(63\) 3.92251 + 6.90028i 0.494190 + 0.869354i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) −6.43177 + 1.13409i −0.797763 + 0.140667i
\(66\) 4.76297 + 0.0329855i 0.586281 + 0.00406023i
\(67\) −1.47671 + 0.537479i −0.180409 + 0.0656635i −0.430645 0.902521i \(-0.641714\pi\)
0.250236 + 0.968185i \(0.419492\pi\)
\(68\) 4.67032 1.69986i 0.566359 0.206138i
\(69\) 7.98581 + 4.68464i 0.961378 + 0.563965i
\(70\) −3.45211 + 9.69996i −0.412606 + 1.15937i
\(71\) 6.90603 + 3.98720i 0.819595 + 0.473194i 0.850277 0.526336i \(-0.176434\pi\)
−0.0306816 + 0.999529i \(0.509768\pi\)
\(72\) −1.96001 + 2.27120i −0.230989 + 0.267664i
\(73\) −1.45847 + 0.842046i −0.170701 + 0.0985541i −0.582916 0.812532i \(-0.698088\pi\)
0.412216 + 0.911086i \(0.364755\pi\)
\(74\) −0.227768 0.271443i −0.0264775 0.0315546i
\(75\) 3.17066 17.2810i 0.366117 1.99544i
\(76\) −7.10463 1.25274i −0.814957 0.143699i
\(77\) 2.53730 + 6.81898i 0.289152 + 0.777094i
\(78\) −0.484933 2.86612i −0.0549078 0.324524i
\(79\) 15.6048 + 5.67967i 1.75567 + 0.639013i 0.999875 0.0157919i \(-0.00502692\pi\)
0.755798 + 0.654805i \(0.227249\pi\)
\(80\) −3.89150 −0.435083
\(81\) 7.05199 5.59191i 0.783554 0.621323i
\(82\) 4.23495i 0.467672i
\(83\) 3.91696 + 1.42566i 0.429943 + 0.156486i 0.547921 0.836530i \(-0.315419\pi\)
−0.117979 + 0.993016i \(0.537641\pi\)
\(84\) −4.30657 1.56635i −0.469885 0.170903i
\(85\) −14.8160 12.4321i −1.60702 1.34845i
\(86\) −9.39692 1.65693i −1.01330 0.178671i
\(87\) −4.33040 0.794527i −0.464268 0.0851822i
\(88\) −2.10660 + 1.76765i −0.224564 + 0.188432i
\(89\) 2.32657 + 4.02974i 0.246616 + 0.427152i 0.962585 0.270981i \(-0.0873480\pi\)
−0.715969 + 0.698133i \(0.754015\pi\)
\(90\) 11.4680 + 2.18630i 1.20883 + 0.230456i
\(91\) 3.82942 2.24760i 0.401432 0.235612i
\(92\) −5.26416 + 0.928214i −0.548827 + 0.0967730i
\(93\) −12.1487 7.12668i −1.25976 0.739002i
\(94\) −2.58549 7.10357i −0.266673 0.732678i
\(95\) 9.60193 + 26.3811i 0.985137 + 2.70664i
\(96\) 0.0119949 1.73201i 0.00122422 0.176772i
\(97\) −8.44682 + 1.48940i −0.857645 + 0.151226i −0.585144 0.810929i \(-0.698962\pi\)
−0.272501 + 0.962155i \(0.587851\pi\)
\(98\) −0.100156 6.99928i −0.0101173 0.707034i
\(99\) 7.20107 4.02560i 0.723735 0.404588i
\(100\) 5.07188 + 8.78475i 0.507188 + 0.878475i
\(101\) 1.34123 1.12543i 0.133457 0.111984i −0.573616 0.819125i \(-0.694460\pi\)
0.707073 + 0.707141i \(0.250015\pi\)
\(102\) 5.57889 6.55592i 0.552392 0.649133i
\(103\) −2.90951 0.513024i −0.286682 0.0505498i 0.0284578 0.999595i \(-0.490940\pi\)
−0.315140 + 0.949045i \(0.602051\pi\)
\(104\) 1.28563 + 1.07877i 0.126066 + 0.105782i
\(105\) 3.10070 + 17.5614i 0.302598 + 1.71382i
\(106\) 6.04625 + 2.20065i 0.587264 + 0.213746i
\(107\) 6.80171i 0.657546i 0.944409 + 0.328773i \(0.106635\pi\)
−0.944409 + 0.328773i \(0.893365\pi\)
\(108\) −1.00841 + 5.09736i −0.0970347 + 0.490494i
\(109\) 14.3654 1.37596 0.687979 0.725731i \(-0.258498\pi\)
0.687979 + 0.725731i \(0.258498\pi\)
\(110\) 10.0561 + 3.66013i 0.958813 + 0.348980i
\(111\) −0.575261 0.213901i −0.0546013 0.0203026i
\(112\) 2.47966 0.922664i 0.234305 0.0871835i
\(113\) 3.25368 + 0.573711i 0.306080 + 0.0539702i 0.324579 0.945859i \(-0.394778\pi\)
−0.0184986 + 0.999829i \(0.505889\pi\)
\(114\) −11.7712 + 4.19227i −1.10247 + 0.392642i
\(115\) 13.3710 + 15.9349i 1.24685 + 1.48594i
\(116\) 2.20134 1.27095i 0.204390 0.118004i
\(117\) −3.18259 3.90134i −0.294230 0.360679i
\(118\) −4.62650 2.67111i −0.425904 0.245896i
\(119\) 12.3884 + 4.40888i 1.13564 + 0.404161i
\(120\) −5.86045 + 3.32963i −0.534983 + 0.303952i
\(121\) −3.23035 + 1.17575i −0.293669 + 0.106887i
\(122\) −4.82291 + 1.75540i −0.436646 + 0.158926i
\(123\) 3.62350 + 6.37768i 0.326720 + 0.575056i
\(124\) 8.00829 1.41208i 0.719166 0.126808i
\(125\) 10.0085 17.3352i 0.895184 1.55050i
\(126\) −7.82572 + 1.32592i −0.697171 + 0.118122i
\(127\) 6.06645 + 10.5074i 0.538310 + 0.932381i 0.998995 + 0.0448173i \(0.0142706\pi\)
−0.460685 + 0.887564i \(0.652396\pi\)
\(128\) 0.642788 + 0.766044i 0.0568149 + 0.0677094i
\(129\) −15.5691 + 5.54489i −1.37078 + 0.488200i
\(130\) 1.13409 6.43177i 0.0994667 0.564103i
\(131\) −17.1170 14.3629i −1.49552 1.25489i −0.887362 0.461073i \(-0.847465\pi\)
−0.608157 0.793817i \(-0.708091\pi\)
\(132\) −1.66003 + 4.46445i −0.144487 + 0.388580i
\(133\) −12.3732 14.5334i −1.07289 1.26020i
\(134\) 1.57148i 0.135755i
\(135\) 19.1409 6.51969i 1.64739 0.561126i
\(136\) 4.97005i 0.426178i
\(137\) −4.31074 + 11.8437i −0.368292 + 1.01187i 0.607719 + 0.794152i \(0.292085\pi\)
−0.976011 + 0.217721i \(0.930138\pi\)
\(138\) −7.13343 + 5.90196i −0.607238 + 0.502408i
\(139\) 8.45500 10.0763i 0.717144 0.854659i −0.277206 0.960810i \(-0.589409\pi\)
0.994350 + 0.106152i \(0.0338529\pi\)
\(140\) −7.93429 6.56150i −0.670570 0.554548i
\(141\) −9.97158 8.48552i −0.839759 0.714610i
\(142\) −6.10875 + 5.12585i −0.512634 + 0.430151i
\(143\) −2.30760 3.99688i −0.192971 0.334236i
\(144\) −1.46387 2.61860i −0.121989 0.218217i
\(145\) −8.56652 4.94588i −0.711411 0.410733i
\(146\) −0.292440 1.65851i −0.0242025 0.137259i
\(147\) −6.13954 10.4550i −0.506380 0.862310i
\(148\) 0.332974 0.121193i 0.0273703 0.00996198i
\(149\) −0.202016 0.555033i −0.0165498 0.0454701i 0.931143 0.364655i \(-0.118813\pi\)
−0.947692 + 0.319185i \(0.896591\pi\)
\(150\) 15.1544 + 8.88991i 1.23735 + 0.725858i
\(151\) −3.14466 17.8343i −0.255909 1.45133i −0.793729 0.608272i \(-0.791863\pi\)
0.537820 0.843060i \(-0.319248\pi\)
\(152\) 3.60712 6.24771i 0.292576 0.506756i
\(153\) 2.79224 14.6464i 0.225739 1.18409i
\(154\) −7.27555 + 0.0520518i −0.586280 + 0.00419445i
\(155\) −20.3410 24.2415i −1.63383 1.94712i
\(156\) 2.85913 + 0.524582i 0.228913 + 0.0420002i
\(157\) 2.28213 + 0.402401i 0.182134 + 0.0321151i 0.263971 0.964531i \(-0.414968\pi\)
−0.0818374 + 0.996646i \(0.526079\pi\)
\(158\) −10.6743 + 12.7211i −0.849201 + 1.01204i
\(159\) 10.9883 1.85917i 0.871432 0.147442i
\(160\) 1.33097 3.65681i 0.105222 0.289096i
\(161\) −12.2981 6.98346i −0.969223 0.550374i
\(162\) 2.84276 + 8.53925i 0.223348 + 0.670907i
\(163\) 16.8886 1.32281 0.661407 0.750027i \(-0.269960\pi\)
0.661407 + 0.750027i \(0.269960\pi\)
\(164\) −3.97955 1.44844i −0.310751 0.113104i
\(165\) 18.2758 3.09217i 1.42277 0.240725i
\(166\) −2.67936 + 3.19314i −0.207959 + 0.247836i
\(167\) 0.610365 3.46155i 0.0472315 0.267863i −0.952042 0.305966i \(-0.901021\pi\)
0.999274 + 0.0381034i \(0.0121316\pi\)
\(168\) 2.94482 3.51113i 0.227198 0.270890i
\(169\) 7.80094 6.54577i 0.600072 0.503521i
\(170\) 16.7497 9.67046i 1.28465 0.741690i
\(171\) −14.1399 + 16.3850i −1.08131 + 1.25299i
\(172\) 4.77094 8.26351i 0.363781 0.630087i
\(173\) 2.05049 + 11.6289i 0.155896 + 0.884130i 0.957962 + 0.286895i \(0.0926230\pi\)
−0.802066 + 0.597235i \(0.796266\pi\)
\(174\) 2.22770 3.79750i 0.168881 0.287888i
\(175\) −4.47114 + 26.4628i −0.337986 + 2.00040i
\(176\) −0.940545 2.58413i −0.0708962 0.194786i
\(177\) −9.25279 0.0640792i −0.695482 0.00481649i
\(178\) −4.58245 + 0.808010i −0.343469 + 0.0605629i
\(179\) −9.62789 5.55866i −0.719622 0.415474i 0.0949914 0.995478i \(-0.469718\pi\)
−0.814614 + 0.580004i \(0.803051\pi\)
\(180\) −5.97672 + 10.0286i −0.445478 + 0.747487i
\(181\) −3.23752 + 1.86918i −0.240643 + 0.138935i −0.615472 0.788159i \(-0.711035\pi\)
0.374829 + 0.927094i \(0.377701\pi\)
\(182\) 0.802312 + 4.36720i 0.0594713 + 0.323719i
\(183\) −5.76118 + 6.77013i −0.425878 + 0.500462i
\(184\) 0.928214 5.26416i 0.0684289 0.388079i
\(185\) −1.05632 0.886357i −0.0776622 0.0651663i
\(186\) 10.8520 8.97856i 0.795706 0.658340i
\(187\) 4.67455 12.8432i 0.341837 0.939189i
\(188\) 7.55946 0.551331
\(189\) −10.6508 + 8.69260i −0.774729 + 0.632294i
\(190\) −28.0742 −2.03671
\(191\) 4.67506 12.8446i 0.338275 0.929404i −0.647608 0.761973i \(-0.724231\pi\)
0.985884 0.167431i \(-0.0535471\pi\)
\(192\) 1.62345 + 0.603654i 0.117163 + 0.0435649i
\(193\) −6.13489 5.14778i −0.441599 0.370545i 0.394709 0.918806i \(-0.370846\pi\)
−0.836307 + 0.548261i \(0.815290\pi\)
\(194\) 1.48940 8.44682i 0.106933 0.606447i
\(195\) −3.79523 10.6563i −0.271782 0.763117i
\(196\) 6.61143 + 2.29978i 0.472245 + 0.164270i
\(197\) 10.5622 6.09810i 0.752527 0.434472i −0.0740793 0.997252i \(-0.523602\pi\)
0.826606 + 0.562781i \(0.190268\pi\)
\(198\) 1.31992 + 8.14363i 0.0938024 + 0.578743i
\(199\) 5.96407 + 3.44336i 0.422781 + 0.244093i 0.696267 0.717783i \(-0.254843\pi\)
−0.273485 + 0.961876i \(0.588176\pi\)
\(200\) −9.98965 + 1.76144i −0.706375 + 0.124553i
\(201\) −1.34459 2.36659i −0.0948398 0.166926i
\(202\) 0.598826 + 1.64526i 0.0421333 + 0.115760i
\(203\) 6.63123 + 1.12041i 0.465421 + 0.0786373i
\(204\) 4.25245 + 7.48470i 0.297731 + 0.524034i
\(205\) 2.86178 + 16.2299i 0.199875 + 1.13355i
\(206\) 1.47720 2.55858i 0.102921 0.178265i
\(207\) −5.69286 + 14.9916i −0.395681 + 1.04199i
\(208\) −1.45343 + 0.839136i −0.100777 + 0.0581836i
\(209\) −15.1975 + 12.7522i −1.05123 + 0.882089i
\(210\) −17.5629 3.09266i −1.21195 0.213414i
\(211\) 2.81430 15.9607i 0.193745 1.09878i −0.720451 0.693506i \(-0.756065\pi\)
0.914195 0.405274i \(-0.132824\pi\)
\(212\) −4.13588 + 4.92895i −0.284053 + 0.338521i
\(213\) −4.81377 + 12.9461i −0.329834 + 0.887050i
\(214\) −6.39152 2.32632i −0.436915 0.159024i
\(215\) −37.1322 −2.53240
\(216\) −4.44506 2.69100i −0.302448 0.183099i
\(217\) 18.7089 + 10.6238i 1.27004 + 0.721192i
\(218\) −4.91326 + 13.4991i −0.332768 + 0.914273i
\(219\) −1.85945 2.24743i −0.125650 0.151867i
\(220\) −6.87879 + 8.19782i −0.463768 + 0.552697i
\(221\) −8.21437 1.44841i −0.552558 0.0974309i
\(222\) 0.397752 0.467410i 0.0266953 0.0313705i
\(223\) 10.8119 + 12.8851i 0.724016 + 0.862849i 0.995014 0.0997312i \(-0.0317983\pi\)
−0.270999 + 0.962580i \(0.587354\pi\)
\(224\) 0.0189281 + 2.64568i 0.00126469 + 0.176772i
\(225\) 30.4283 + 0.421477i 2.02856 + 0.0280985i
\(226\) −1.65193 + 2.86123i −0.109885 + 0.190326i
\(227\) −3.32251 18.8429i −0.220523 1.25065i −0.871062 0.491173i \(-0.836568\pi\)
0.650539 0.759473i \(-0.274543\pi\)
\(228\) 0.0865337 12.4951i 0.00573083 0.827509i
\(229\) −2.45664 6.74955i −0.162339 0.446023i 0.831677 0.555260i \(-0.187381\pi\)
−0.994016 + 0.109237i \(0.965159\pi\)
\(230\) −19.5470 + 7.11453i −1.28889 + 0.469118i
\(231\) −10.9122 + 6.30347i −0.717967 + 0.414738i
\(232\) 0.441395 + 2.50327i 0.0289790 + 0.164348i
\(233\) −12.2778 7.08860i −0.804346 0.464389i 0.0406425 0.999174i \(-0.487060\pi\)
−0.844989 + 0.534784i \(0.820393\pi\)
\(234\) 4.75457 1.65632i 0.310816 0.108277i
\(235\) −14.7088 25.4764i −0.959498 1.66190i
\(236\) 4.09238 3.43392i 0.266391 0.223529i
\(237\) −5.19066 + 28.2906i −0.337170 + 1.83767i
\(238\) −8.38006 + 10.1333i −0.543198 + 0.656845i
\(239\) −3.51743 + 4.19191i −0.227523 + 0.271152i −0.867713 0.497065i \(-0.834411\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(240\) −1.12444 6.64582i −0.0725822 0.428986i
\(241\) −0.722609 + 1.98535i −0.0465474 + 0.127888i −0.960788 0.277283i \(-0.910566\pi\)
0.914241 + 0.405171i \(0.132788\pi\)
\(242\) 3.43767i 0.220982i
\(243\) 11.5874 + 10.4275i 0.743332 + 0.668922i
\(244\) 5.13244i 0.328571i
\(245\) −5.11361 26.7562i −0.326697 1.70939i
\(246\) −7.23237 + 1.22368i −0.461119 + 0.0780190i
\(247\) 9.27484 + 7.78251i 0.590144 + 0.495189i
\(248\) −1.41208 + 8.00829i −0.0896670 + 0.508527i
\(249\) −1.30291 + 7.10125i −0.0825687 + 0.450023i
\(250\) 12.8666 + 15.3338i 0.813757 + 0.969797i
\(251\) 0.00894719 + 0.0154970i 0.000564742 + 0.000978161i 0.866308 0.499511i \(-0.166487\pi\)
−0.865743 + 0.500489i \(0.833154\pi\)
\(252\) 1.43060 7.80726i 0.0901194 0.491811i
\(253\) −7.34980 + 12.7302i −0.462078 + 0.800343i
\(254\) −11.9486 + 2.10686i −0.749720 + 0.132196i
\(255\) 16.9502 28.8947i 1.06147 1.80946i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 18.6003 6.76995i 1.16025 0.422298i 0.311066 0.950388i \(-0.399314\pi\)
0.849188 + 0.528090i \(0.177092\pi\)
\(258\) 0.114454 16.5266i 0.00712557 1.02890i
\(259\) 0.883238 + 0.314335i 0.0548817 + 0.0195318i
\(260\) 5.65600 + 3.26549i 0.350770 + 0.202517i
\(261\) 0.105617 7.62494i 0.00653751 0.471972i
\(262\) 19.3510 11.1723i 1.19551 0.690229i
\(263\) 6.42905 + 7.66185i 0.396432 + 0.472450i 0.926929 0.375237i \(-0.122439\pi\)
−0.530496 + 0.847687i \(0.677994\pi\)
\(264\) −3.62745 3.08685i −0.223254 0.189982i
\(265\) 24.6586 + 4.34798i 1.51477 + 0.267094i
\(266\) 17.8888 6.65631i 1.09683 0.408125i
\(267\) −6.20965 + 5.13766i −0.380024 + 0.314419i
\(268\) 1.47671 + 0.537479i 0.0902044 + 0.0328317i
\(269\) 26.7576 1.63144 0.815720 0.578447i \(-0.196341\pi\)
0.815720 + 0.578447i \(0.196341\pi\)
\(270\) −0.420075 + 20.2165i −0.0255649 + 1.23033i
\(271\) 26.6221i 1.61718i −0.588373 0.808590i \(-0.700231\pi\)
0.588373 0.808590i \(-0.299769\pi\)
\(272\) −4.67032 1.69986i −0.283179 0.103069i
\(273\) 4.94490 + 5.89037i 0.299279 + 0.356501i
\(274\) −9.65505 8.10155i −0.583283 0.489433i
\(275\) 27.4712 + 4.84392i 1.65658 + 0.292099i
\(276\) −3.10625 8.72182i −0.186974 0.524992i
\(277\) −11.8133 + 9.91258i −0.709795 + 0.595589i −0.924542 0.381081i \(-0.875552\pi\)
0.214746 + 0.976670i \(0.431108\pi\)
\(278\) 6.57682 + 11.3914i 0.394452 + 0.683210i
\(279\) 8.66046 22.8065i 0.518488 1.36539i
\(280\) 8.87948 5.21163i 0.530651 0.311454i
\(281\) −24.7789 + 4.36919i −1.47819 + 0.260644i −0.853853 0.520514i \(-0.825740\pi\)
−0.624334 + 0.781158i \(0.714629\pi\)
\(282\) 11.3843 6.46800i 0.677923 0.385164i
\(283\) −4.29784 11.8082i −0.255480 0.701926i −0.999432 0.0336931i \(-0.989273\pi\)
0.743952 0.668233i \(-0.232949\pi\)
\(284\) −2.72741 7.49349i −0.161842 0.444657i
\(285\) −42.2786 + 24.0207i −2.50437 + 1.42287i
\(286\) 4.54508 0.801420i 0.268756 0.0473890i
\(287\) −5.67159 9.66317i −0.334784 0.570399i
\(288\) 2.96136 0.479975i 0.174500 0.0282828i
\(289\) −3.85068 6.66957i −0.226510 0.392327i
\(290\) 7.57753 6.35831i 0.444968 0.373373i
\(291\) −4.98426 13.9949i −0.292183 0.820398i
\(292\) 1.65851 + 0.292440i 0.0970568 + 0.0171137i
\(293\) 10.1575 + 8.52312i 0.593405 + 0.497926i 0.889318 0.457289i \(-0.151179\pi\)
−0.295913 + 0.955215i \(0.595624\pi\)
\(294\) 11.9243 2.19347i 0.695439 0.127926i
\(295\) −19.5355 7.11035i −1.13740 0.413980i
\(296\) 0.354344i 0.0205958i
\(297\) 8.95558 + 11.1347i 0.519655 + 0.646098i
\(298\) 0.590654 0.0342157
\(299\) 8.42997 + 3.06826i 0.487518 + 0.177442i
\(300\) −13.5369 + 11.2000i −0.781554 + 0.646631i
\(301\) 23.6606 8.80395i 1.36377 0.507451i
\(302\) 17.8343 + 3.14466i 1.02625 + 0.180955i
\(303\) 2.30952 + 1.96533i 0.132679 + 0.112906i
\(304\) 4.63722 + 5.52642i 0.265963 + 0.316962i
\(305\) −17.2970 + 9.98644i −0.990424 + 0.571822i
\(306\) 12.8081 + 7.63319i 0.732188 + 0.436361i
\(307\) 15.3747 + 8.87658i 0.877480 + 0.506613i 0.869827 0.493357i \(-0.164231\pi\)
0.00765328 + 0.999971i \(0.497564\pi\)
\(308\) 2.43947 6.85458i 0.139002 0.390576i
\(309\) 0.0354375 5.11703i 0.00201597 0.291098i
\(310\) 29.7366 10.8232i 1.68892 0.614718i
\(311\) 26.0813 9.49283i 1.47894 0.538289i 0.528425 0.848980i \(-0.322783\pi\)
0.950511 + 0.310691i \(0.100560\pi\)
\(312\) −1.47082 + 2.50728i −0.0832690 + 0.141947i
\(313\) −27.7620 + 4.89518i −1.56920 + 0.276692i −0.889547 0.456843i \(-0.848980\pi\)
−0.679652 + 0.733535i \(0.737869\pi\)
\(314\) −1.15867 + 2.00687i −0.0653873 + 0.113254i
\(315\) −29.0951 + 10.3697i −1.63933 + 0.584264i
\(316\) −8.30312 14.3814i −0.467087 0.809019i
\(317\) 6.01723 + 7.17106i 0.337962 + 0.402767i 0.908081 0.418795i \(-0.137547\pi\)
−0.570119 + 0.821562i \(0.693103\pi\)
\(318\) −2.01118 + 10.9615i −0.112782 + 0.614692i
\(319\) 1.21382 6.88393i 0.0679610 0.385426i
\(320\) 2.98106 + 2.50141i 0.166646 + 0.139833i
\(321\) −11.6158 + 1.96534i −0.648332 + 0.109695i
\(322\) 10.7685 9.16792i 0.600105 0.510908i
\(323\) 35.8551i 1.99503i
\(324\) −8.99655 0.249279i −0.499808 0.0138488i
\(325\) 17.0240i 0.944320i
\(326\) −5.77623 + 15.8701i −0.319916 + 0.878961i
\(327\) 4.15085 + 24.5330i 0.229543 + 1.35668i
\(328\) 2.72218 3.24416i 0.150307 0.179129i
\(329\) 15.4128 + 12.7461i 0.849737 + 0.702716i
\(330\) −3.34500 + 18.2312i −0.184136 + 1.00360i
\(331\) 15.4208 12.9396i 0.847601 0.711222i −0.111659 0.993747i \(-0.535616\pi\)
0.959260 + 0.282525i \(0.0911719\pi\)
\(332\) −2.08417 3.60989i −0.114384 0.198119i
\(333\) 0.199075 1.04422i 0.0109092 0.0572231i
\(334\) 3.04404 + 1.75748i 0.166562 + 0.0961648i
\(335\) −1.06193 6.02251i −0.0580195 0.329045i
\(336\) 2.29220 + 3.96810i 0.125050 + 0.216478i
\(337\) 20.6806 7.52714i 1.12655 0.410029i 0.289509 0.957175i \(-0.406508\pi\)
0.837037 + 0.547146i \(0.184286\pi\)
\(338\) 3.48293 + 9.56927i 0.189446 + 0.520500i
\(339\) −0.0396294 + 5.72233i −0.00215238 + 0.310794i
\(340\) 3.35852 + 19.0471i 0.182141 + 1.03297i
\(341\) 11.1811 19.3663i 0.605493 1.04874i
\(342\) −10.5607 18.8912i −0.571058 1.02152i
\(343\) 9.60221 + 15.8366i 0.518471 + 0.855095i
\(344\) 6.13340 + 7.30951i 0.330691 + 0.394102i
\(345\) −23.3497 + 27.4390i −1.25711 + 1.47726i
\(346\) −11.6289 2.05049i −0.625174 0.110235i
\(347\) −15.6453 + 18.6454i −0.839884 + 1.00094i 0.160020 + 0.987114i \(0.448844\pi\)
−0.999904 + 0.0138213i \(0.995600\pi\)
\(348\) 2.80657 + 3.39217i 0.150448 + 0.181839i
\(349\) 6.00922 16.5102i 0.321666 0.883770i −0.668480 0.743730i \(-0.733055\pi\)
0.990146 0.140040i \(-0.0447230\pi\)
\(350\) −23.3377 13.2523i −1.24745 0.708365i
\(351\) 5.74303 6.56244i 0.306540 0.350277i
\(352\) 2.74997 0.146574
\(353\) −11.2811 4.10598i −0.600432 0.218539i 0.0238797 0.999715i \(-0.492398\pi\)
−0.624311 + 0.781176i \(0.714620\pi\)
\(354\) 3.22485 8.67286i 0.171399 0.460957i
\(355\) −19.9472 + 23.7722i −1.05869 + 1.26170i
\(356\) 0.808010 4.58245i 0.0428245 0.242870i
\(357\) −3.94981 + 22.4305i −0.209046 + 1.18715i
\(358\) 8.51637 7.14608i 0.450104 0.377682i
\(359\) −13.3990 + 7.73591i −0.707172 + 0.408286i −0.810013 0.586412i \(-0.800540\pi\)
0.102841 + 0.994698i \(0.467207\pi\)
\(360\) −7.37964 9.04626i −0.388941 0.476780i
\(361\) 16.5226 28.6179i 0.869609 1.50621i
\(362\) −0.649161 3.68157i −0.0341191 0.193499i
\(363\) −2.94133 5.17700i −0.154380 0.271722i
\(364\) −4.37824 0.739744i −0.229482 0.0387731i
\(365\) −2.24148 6.15841i −0.117324 0.322346i
\(366\) −4.39140 7.72926i −0.229542 0.404015i
\(367\) 13.6855 2.41312i 0.714377 0.125964i 0.195365 0.980731i \(-0.437411\pi\)
0.519012 + 0.854767i \(0.326300\pi\)
\(368\) 4.62923 + 2.67269i 0.241315 + 0.139323i
\(369\) −9.84466 + 8.03095i −0.512493 + 0.418074i
\(370\) 1.19419 0.689464i 0.0620828 0.0358435i
\(371\) −16.7433 + 3.07597i −0.869269 + 0.159696i
\(372\) 4.72549 + 13.2684i 0.245005 + 0.687933i
\(373\) −5.89351 + 33.4238i −0.305154 + 1.73062i 0.317623 + 0.948217i \(0.397115\pi\)
−0.622777 + 0.782399i \(0.713996\pi\)
\(374\) 10.4699 + 8.78528i 0.541385 + 0.454276i
\(375\) 32.4965 + 12.0833i 1.67811 + 0.623978i
\(376\) −2.58549 + 7.10357i −0.133336 + 0.366339i
\(377\) −4.26598 −0.219709
\(378\) −4.52560 12.9815i −0.232772 0.667696i
\(379\) 5.88433 0.302258 0.151129 0.988514i \(-0.451709\pi\)
0.151129 + 0.988514i \(0.451709\pi\)
\(380\) 9.60193 26.3811i 0.492569 1.35332i
\(381\) −16.1914 + 13.3962i −0.829512 + 0.686311i
\(382\) 10.4710 + 8.78624i 0.535744 + 0.449543i
\(383\) 3.97094 22.5203i 0.202906 1.15074i −0.697796 0.716297i \(-0.745836\pi\)
0.900701 0.434439i \(-0.143053\pi\)
\(384\) −1.12250 + 1.31909i −0.0572825 + 0.0673143i
\(385\) −27.8475 + 5.11594i −1.41924 + 0.260733i
\(386\) 6.93559 4.00426i 0.353012 0.203812i
\(387\) −13.9681 24.9864i −0.710038 1.27013i
\(388\) 7.42801 + 4.28856i 0.377100 + 0.217719i
\(389\) 34.5428 6.09083i 1.75139 0.308818i 0.796250 0.604968i \(-0.206814\pi\)
0.955141 + 0.296150i \(0.0957029\pi\)
\(390\) 11.3117 + 0.0783383i 0.572792 + 0.00396681i
\(391\) 9.08636 + 24.9646i 0.459517 + 1.26251i
\(392\) −4.42233 + 5.42614i −0.223361 + 0.274062i
\(393\) 19.5827 33.3822i 0.987816 1.68391i
\(394\) 2.11785 + 12.0109i 0.106696 + 0.605101i
\(395\) −32.3116 + 55.9653i −1.62577 + 2.81592i
\(396\) −8.10395 1.54497i −0.407239 0.0776377i
\(397\) −9.45939 + 5.46138i −0.474753 + 0.274099i −0.718227 0.695809i \(-0.755046\pi\)
0.243474 + 0.969907i \(0.421713\pi\)
\(398\) −5.27553 + 4.42669i −0.264438 + 0.221890i
\(399\) 21.2446 25.3301i 1.06356 1.26809i
\(400\) 1.76144 9.98965i 0.0880722 0.499482i
\(401\) −3.54267 + 4.22199i −0.176912 + 0.210836i −0.847212 0.531254i \(-0.821721\pi\)
0.670300 + 0.742090i \(0.266165\pi\)
\(402\) 2.68374 0.454076i 0.133853 0.0226473i
\(403\) −12.8244 4.66769i −0.638828 0.232514i
\(404\) −1.75085 −0.0871081
\(405\) 16.6649 + 30.8046i 0.828086 + 1.53069i
\(406\) −3.32085 + 5.84811i −0.164811 + 0.290237i
\(407\) 0.333276 0.915668i 0.0165199 0.0453880i
\(408\) −8.48774 + 1.43608i −0.420206 + 0.0710967i
\(409\) −9.82756 + 11.7120i −0.485942 + 0.579123i −0.952180 0.305536i \(-0.901164\pi\)
0.466239 + 0.884659i \(0.345609\pi\)
\(410\) −16.2299 2.86178i −0.801540 0.141333i
\(411\) −21.4720 3.93960i −1.05913 0.194326i
\(412\) 1.89905 + 2.26319i 0.0935593 + 0.111500i
\(413\) 14.1338 0.101118i 0.695481 0.00497571i
\(414\) −12.1404 10.4770i −0.596670 0.514915i
\(415\) −8.11055 + 14.0479i −0.398131 + 0.689584i
\(416\) −0.291429 1.65277i −0.0142885 0.0810339i
\(417\) 19.6511 + 11.5278i 0.962319 + 0.564517i
\(418\) −6.78531 18.6425i −0.331880 0.911834i
\(419\) −7.80252 + 2.83989i −0.381178 + 0.138738i −0.525501 0.850793i \(-0.676122\pi\)
0.144322 + 0.989531i \(0.453900\pi\)
\(420\) 8.91301 15.4459i 0.434910 0.753685i
\(421\) 3.40910 + 19.3340i 0.166149 + 0.942280i 0.947871 + 0.318653i \(0.103230\pi\)
−0.781722 + 0.623627i \(0.785658\pi\)
\(422\) 14.0356 + 8.10346i 0.683242 + 0.394470i
\(423\) 11.6101 19.4811i 0.564504 0.947205i
\(424\) −3.21714 5.57225i −0.156238 0.270613i
\(425\) 38.6201 32.4061i 1.87335 1.57193i
\(426\) −10.5189 8.95129i −0.509643 0.433691i
\(427\) 8.65387 10.4644i 0.418790 0.506409i
\(428\) 4.37206 5.21041i 0.211331 0.251855i
\(429\) 6.15901 5.09575i 0.297360 0.246025i
\(430\) 12.7000 34.8929i 0.612447 1.68268i
\(431\) 15.3638i 0.740050i 0.929022 + 0.370025i \(0.120651\pi\)
−0.929022 + 0.370025i \(0.879349\pi\)
\(432\) 4.04901 3.25661i 0.194808 0.156684i
\(433\) 10.6521i 0.511908i 0.966689 + 0.255954i \(0.0823895\pi\)
−0.966689 + 0.255954i \(0.917610\pi\)
\(434\) −16.3819 + 13.9470i −0.786358 + 0.669478i
\(435\) 5.97120 16.0588i 0.286297 0.769962i
\(436\) −11.0045 9.23391i −0.527022 0.442224i
\(437\) 6.69635 37.9769i 0.320330 1.81668i
\(438\) 2.74786 0.978644i 0.131298 0.0467614i
\(439\) 12.7922 + 15.2452i 0.610540 + 0.727613i 0.979413 0.201867i \(-0.0647009\pi\)
−0.368873 + 0.929480i \(0.620256\pi\)
\(440\) −5.35075 9.26777i −0.255087 0.441824i
\(441\) 16.0808 13.5059i 0.765750 0.643138i
\(442\) 4.17054 7.22359i 0.198372 0.343591i
\(443\) −17.4953 + 3.08489i −0.831225 + 0.146567i −0.573039 0.819528i \(-0.694236\pi\)
−0.258186 + 0.966095i \(0.583125\pi\)
\(444\) 0.303182 + 0.533628i 0.0143884 + 0.0253249i
\(445\) −17.0157 + 6.19320i −0.806620 + 0.293586i
\(446\) −15.8059 + 5.75287i −0.748430 + 0.272406i
\(447\) 0.889502 0.505373i 0.0420720 0.0239033i
\(448\) −2.49260 0.887090i −0.117764 0.0419111i
\(449\) −8.15435 4.70791i −0.384827 0.222180i 0.295089 0.955470i \(-0.404651\pi\)
−0.679917 + 0.733290i \(0.737984\pi\)
\(450\) −10.8032 + 28.4491i −0.509266 + 1.34111i
\(451\) −10.0857 + 5.82300i −0.474918 + 0.274194i
\(452\) −2.12369 2.53091i −0.0998898 0.119044i
\(453\) 29.5483 10.5236i 1.38830 0.494440i
\(454\) 18.8429 + 3.32251i 0.884340 + 0.155933i
\(455\) 6.02591 + 16.1946i 0.282499 + 0.759215i
\(456\) 11.7120 + 4.35490i 0.548463 + 0.203937i
\(457\) −24.5535 8.93673i −1.14856 0.418043i −0.303564 0.952811i \(-0.598177\pi\)
−0.844999 + 0.534768i \(0.820399\pi\)
\(458\) 7.18272 0.335627
\(459\) 25.8195 + 0.536501i 1.20515 + 0.0250417i
\(460\) 20.8015i 0.969875i
\(461\) −1.47622 0.537300i −0.0687543 0.0250245i 0.307414 0.951576i \(-0.400536\pi\)
−0.376168 + 0.926551i \(0.622759\pi\)
\(462\) −2.19115 12.4100i −0.101941 0.577365i
\(463\) 2.89321 + 2.42769i 0.134459 + 0.112824i 0.707537 0.706677i \(-0.249806\pi\)
−0.573078 + 0.819501i \(0.694251\pi\)
\(464\) −2.50327 0.441395i −0.116212 0.0204912i
\(465\) 35.5216 41.7425i 1.64728 1.93576i
\(466\) 10.8604 9.11292i 0.503096 0.422148i
\(467\) 15.5675 + 26.9637i 0.720377 + 1.24773i 0.960849 + 0.277074i \(0.0893646\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(468\) −0.0697329 + 5.03433i −0.00322340 + 0.232712i
\(469\) 2.10458 + 3.58575i 0.0971806 + 0.165575i
\(470\) 28.9707 5.10832i 1.33632 0.235629i
\(471\) −0.0277961 + 4.01364i −0.00128078 + 0.184939i
\(472\) 1.82715 + 5.02005i 0.0841014 + 0.231067i
\(473\) −8.97457 24.6574i −0.412651 1.13375i
\(474\) −24.8092 14.5536i −1.13952 0.668468i
\(475\) −72.0676 + 12.7075i −3.30669 + 0.583059i
\(476\) −6.65605 11.3405i −0.305080 0.519790i
\(477\) 6.35011 + 18.2284i 0.290751 + 0.834623i
\(478\) −2.73607 4.73902i −0.125145 0.216758i
\(479\) −6.19661 + 5.19957i −0.283130 + 0.237574i −0.773281 0.634063i \(-0.781386\pi\)
0.490151 + 0.871637i \(0.336942\pi\)
\(480\) 6.62961 + 1.21638i 0.302599 + 0.0555197i
\(481\) −0.585650 0.103266i −0.0267033 0.00470852i
\(482\) −1.61847 1.35806i −0.0737195 0.0618580i
\(483\) 8.37271 23.0202i 0.380972 1.04746i
\(484\) 3.23035 + 1.17575i 0.146834 + 0.0534433i
\(485\) 33.3779i 1.51561i
\(486\) −13.7617 + 7.32219i −0.624245 + 0.332141i
\(487\) −18.0725 −0.818945 −0.409472 0.912323i \(-0.634287\pi\)
−0.409472 + 0.912323i \(0.634287\pi\)
\(488\) 4.82291 + 1.75540i 0.218323 + 0.0794631i
\(489\) 4.87991 + 28.8419i 0.220677 + 1.30428i
\(490\) 26.8916 + 4.34594i 1.21484 + 0.196330i
\(491\) 9.13275 + 1.61035i 0.412155 + 0.0726741i 0.375881 0.926668i \(-0.377340\pi\)
0.0362739 + 0.999342i \(0.488451\pi\)
\(492\) 1.32373 7.21472i 0.0596784 0.325265i
\(493\) −8.12054 9.67768i −0.365731 0.435861i
\(494\) −10.4854 + 6.05372i −0.471758 + 0.272370i
\(495\) 10.5615 + 30.3175i 0.474704 + 1.36267i
\(496\) −7.04237 4.06592i −0.316212 0.182565i
\(497\) 7.07401 19.8770i 0.317313 0.891606i
\(498\) −6.22737 3.65311i −0.279055 0.163700i
\(499\) −24.0969 + 8.77057i −1.07873 + 0.392625i −0.819434 0.573174i \(-0.805712\pi\)
−0.259293 + 0.965799i \(0.583490\pi\)
\(500\) −18.8097 + 6.84619i −0.841197 + 0.306171i
\(501\) 6.08793 + 0.0421613i 0.271989 + 0.00188363i
\(502\) −0.0176225 + 0.00310733i −0.000786532 + 0.000138687i
\(503\) 5.40271 9.35777i 0.240895 0.417242i −0.720075 0.693897i \(-0.755892\pi\)
0.960969 + 0.276655i \(0.0892258\pi\)
\(504\) 6.84713 + 4.01457i 0.304996 + 0.178823i
\(505\) 3.40672 + 5.90061i 0.151597 + 0.262573i
\(506\) −9.44873 11.2606i −0.420047 0.500593i
\(507\) 13.4328 + 11.4309i 0.596571 + 0.507664i
\(508\) 2.10686 11.9486i 0.0934766 0.530132i
\(509\) −10.9511 9.18908i −0.485400 0.407299i 0.366974 0.930231i \(-0.380394\pi\)
−0.852374 + 0.522932i \(0.824838\pi\)
\(510\) 21.3548 + 25.8106i 0.945607 + 1.14291i
\(511\) 2.88841 + 3.39268i 0.127776 + 0.150083i
\(512\) 1.00000i 0.0441942i
\(513\) −32.0677 19.4135i −1.41582 0.857127i
\(514\) 19.7940i 0.873076i
\(515\) 3.93221 10.8036i 0.173274 0.476066i
\(516\) 15.4908 + 5.75999i 0.681945 + 0.253569i
\(517\) 13.3625 15.9248i 0.587680 0.700370i
\(518\) −0.597463 + 0.722463i −0.0262510 + 0.0317432i
\(519\) −19.2671 + 6.86193i −0.845733 + 0.301206i
\(520\) −5.00303 + 4.19804i −0.219397 + 0.184096i
\(521\) −3.15077 5.45729i −0.138038 0.239088i 0.788716 0.614758i \(-0.210746\pi\)
−0.926754 + 0.375669i \(0.877413\pi\)
\(522\) 7.12898 + 2.70713i 0.312027 + 0.118488i
\(523\) −7.93681 4.58232i −0.347052 0.200371i 0.316334 0.948648i \(-0.397548\pi\)
−0.663386 + 0.748277i \(0.730881\pi\)
\(524\) 3.88011 + 22.0052i 0.169503 + 0.961301i
\(525\) −46.4845 + 0.0106420i −2.02875 + 0.000464457i
\(526\) −9.39865 + 3.42083i −0.409801 + 0.149155i
\(527\) −13.8229 37.9782i −0.602137 1.65436i
\(528\) 4.14135 2.35292i 0.180229 0.102398i
\(529\) −0.967743 5.48834i −0.0420758 0.238624i
\(530\) −12.5195 + 21.6844i −0.543812 + 0.941911i
\(531\) −2.56414 15.8202i −0.111274 0.686539i
\(532\) 0.136552 + 19.0866i 0.00592028 + 0.827508i
\(533\) 4.56855 + 5.44459i 0.197886 + 0.235831i
\(534\) −2.70399 7.59235i −0.117013 0.328553i
\(535\) −26.0667 4.59627i −1.12696 0.198714i
\(536\) −1.01013 + 1.20383i −0.0436309 + 0.0519973i
\(537\) 6.71101 18.0485i 0.289602 0.778849i
\(538\) −9.15164 + 25.1439i −0.394555 + 1.08403i
\(539\) 16.5314 9.86243i 0.712057 0.424805i
\(540\) −18.8536 7.30917i −0.811329 0.314537i
\(541\) 2.09293 0.0899820 0.0449910 0.998987i \(-0.485674\pi\)
0.0449910 + 0.998987i \(0.485674\pi\)
\(542\) 25.0166 + 9.10531i 1.07456 + 0.391106i
\(543\) −4.12763 4.98888i −0.177134 0.214093i
\(544\) 3.19468 3.80728i 0.136971 0.163236i
\(545\) −9.70745 + 55.0537i −0.415822 + 2.35824i
\(546\) −7.22639 + 2.63206i −0.309261 + 0.112642i
\(547\) −6.22461 + 5.22307i −0.266145 + 0.223322i −0.766087 0.642736i \(-0.777799\pi\)
0.499942 + 0.866059i \(0.333355\pi\)
\(548\) 10.9152 6.30189i 0.466274 0.269203i
\(549\) −13.2266 7.88260i −0.564496 0.336421i
\(550\) −13.9475 + 24.1578i −0.594724 + 1.03009i
\(551\) 3.18433 + 18.0592i 0.135657 + 0.769348i
\(552\) 9.25824 + 0.0641170i 0.394057 + 0.00272900i
\(553\) 7.31966 43.3220i 0.311264 1.84224i
\(554\) −5.27437 14.4912i −0.224087 0.615673i
\(555\) 1.20848 2.06007i 0.0512972 0.0874452i
\(556\) −12.9538 + 2.28411i −0.549364 + 0.0968677i
\(557\) −2.48334 1.43375i −0.105222 0.0607501i 0.446465 0.894801i \(-0.352683\pi\)
−0.551688 + 0.834051i \(0.686016\pi\)
\(558\) 18.4691 + 15.9385i 0.781858 + 0.674728i
\(559\) −13.8684 + 8.00693i −0.586572 + 0.338657i
\(560\) 1.86036 + 10.1265i 0.0786147 + 0.427921i
\(561\) 23.2841 + 4.27208i 0.983055 + 0.180367i
\(562\) 4.36919 24.7789i 0.184303 1.04524i
\(563\) −14.5659 12.2222i −0.613878 0.515105i 0.281994 0.959416i \(-0.409004\pi\)
−0.895873 + 0.444311i \(0.853449\pi\)
\(564\) 2.18429 + 12.9099i 0.0919752 + 0.543605i
\(565\) −4.39735 + 12.0816i −0.184998 + 0.508278i
\(566\) 12.5661 0.528191
\(567\) −17.9226 15.6774i −0.752676 0.658391i
\(568\) 7.97440 0.334598
\(569\) −2.25815 + 6.20422i −0.0946667 + 0.260095i −0.977984 0.208682i \(-0.933083\pi\)
0.883317 + 0.468776i \(0.155305\pi\)
\(570\) −8.11196 47.9445i −0.339773 2.00817i
\(571\) −2.31409 1.94175i −0.0968415 0.0812597i 0.593081 0.805142i \(-0.297911\pi\)
−0.689923 + 0.723883i \(0.742356\pi\)
\(572\) −0.801420 + 4.54508i −0.0335091 + 0.190039i
\(573\) 23.2866 + 4.27255i 0.972812 + 0.178488i
\(574\) 11.0202 2.02456i 0.459975 0.0845034i
\(575\) −46.9578 + 27.1111i −1.95827 + 1.13061i
\(576\) −0.561814 + 2.94692i −0.0234089 + 0.122789i
\(577\) −23.9090 13.8039i −0.995344 0.574662i −0.0884765 0.996078i \(-0.528200\pi\)
−0.906867 + 0.421416i \(0.861533\pi\)
\(578\) 7.58435 1.33733i 0.315467 0.0556254i
\(579\) 7.01861 11.9645i 0.291683 0.497226i
\(580\) 3.38318 + 9.29522i 0.140479 + 0.385963i
\(581\) 1.83731 10.8743i 0.0762246 0.451141i
\(582\) 14.8557 + 0.102881i 0.615787 + 0.00426457i
\(583\) 3.07254 + 17.4253i 0.127252 + 0.721681i
\(584\) −0.842046 + 1.45847i −0.0348441 + 0.0603518i
\(585\) 17.1021 9.56054i 0.707083 0.395279i
\(586\) −11.4832 + 6.62981i −0.474366 + 0.273875i
\(587\) −2.43294 + 2.04148i −0.100418 + 0.0842609i −0.691615 0.722267i \(-0.743100\pi\)
0.591196 + 0.806528i \(0.298656\pi\)
\(588\) −2.01716 + 11.9554i −0.0831863 + 0.493031i
\(589\) −10.1871 + 57.7737i −0.419750 + 2.38052i
\(590\) 13.3631 15.9255i 0.550149 0.655642i
\(591\) 13.4661 + 16.2759i 0.553923 + 0.669501i
\(592\) −0.332974 0.121193i −0.0136852 0.00498099i
\(593\) −18.0122 −0.739672 −0.369836 0.929097i \(-0.620586\pi\)
−0.369836 + 0.929097i \(0.620586\pi\)
\(594\) −13.5261 + 4.60721i −0.554984 + 0.189036i
\(595\) −25.2679 + 44.4975i −1.03588 + 1.82422i
\(596\) −0.202016 + 0.555033i −0.00827488 + 0.0227350i
\(597\) −4.15719 + 11.1803i −0.170142 + 0.457577i
\(598\) −5.76644 + 6.87217i −0.235807 + 0.281024i
\(599\) 25.1383 + 4.43257i 1.02712 + 0.181110i 0.661729 0.749743i \(-0.269823\pi\)
0.365395 + 0.930853i \(0.380934\pi\)
\(600\) −5.89464 16.5511i −0.240648 0.675698i
\(601\) 11.3131 + 13.4824i 0.461469 + 0.549958i 0.945725 0.324969i \(-0.105354\pi\)
−0.484255 + 0.874927i \(0.660909\pi\)
\(602\) 0.180610 + 25.2448i 0.00736112 + 1.02890i
\(603\) 3.65310 2.98008i 0.148766 0.121358i
\(604\) −9.05469 + 15.6832i −0.368430 + 0.638140i
\(605\) −2.32301 13.1745i −0.0944438 0.535618i
\(606\) −2.63671 + 1.49806i −0.107109 + 0.0608544i
\(607\) −2.13495 5.86573i −0.0866550 0.238083i 0.888795 0.458306i \(-0.151544\pi\)
−0.975449 + 0.220223i \(0.929321\pi\)
\(608\) −6.77916 + 2.46741i −0.274931 + 0.100067i
\(609\) 0.00266676 + 11.6484i 0.000108062 + 0.472017i
\(610\) −3.46825 19.6694i −0.140425 0.796392i
\(611\) −10.9871 6.34342i −0.444491 0.256627i
\(612\) −11.5535 + 9.42494i −0.467021 + 0.380981i
\(613\) −0.906241 1.56966i −0.0366027 0.0633978i 0.847144 0.531364i \(-0.178320\pi\)
−0.883746 + 0.467966i \(0.844987\pi\)
\(614\) −13.5997 + 11.4115i −0.548840 + 0.460531i
\(615\) −26.8902 + 9.57688i −1.08432 + 0.386177i
\(616\) 5.60685 + 4.63676i 0.225906 + 0.186820i
\(617\) −24.8564 + 29.6227i −1.00068 + 1.19256i −0.0194332 + 0.999811i \(0.506186\pi\)
−0.981247 + 0.192753i \(0.938258\pi\)
\(618\) 4.79632 + 1.78343i 0.192936 + 0.0717400i
\(619\) 4.30111 11.8172i 0.172876 0.474973i −0.822750 0.568404i \(-0.807561\pi\)
0.995626 + 0.0934307i \(0.0297834\pi\)
\(620\) 31.6450i 1.27089i
\(621\) −27.2473 5.39035i −1.09340 0.216307i
\(622\) 27.7552i 1.11288i
\(623\) 9.37397 7.98067i 0.375560 0.319739i
\(624\) −1.85302 2.23966i −0.0741803 0.0896583i
\(625\) 20.8188 + 17.4690i 0.832751 + 0.698761i
\(626\) 4.89518 27.7620i 0.195651 1.10959i
\(627\) −26.1692 22.2692i −1.04510 0.889348i
\(628\) −1.48955 1.77518i −0.0594396 0.0708374i
\(629\) −0.880552 1.52516i −0.0351099 0.0608121i
\(630\) 0.206834 30.8871i 0.00824047 1.23057i
\(631\) 4.91349 8.51042i 0.195603 0.338795i −0.751495 0.659739i \(-0.770667\pi\)
0.947098 + 0.320944i \(0.104000\pi\)
\(632\) 16.3540 2.88364i 0.650526 0.114705i
\(633\) 28.0705 + 0.194400i 1.11570 + 0.00772669i
\(634\) −8.79661 + 3.20170i −0.349358 + 0.127156i
\(635\) −44.3677 + 16.1485i −1.76068 + 0.640835i
\(636\) −9.61260 5.63896i −0.381165 0.223599i
\(637\) −7.67939 8.89045i −0.304269 0.352252i
\(638\) 6.05362 + 3.49506i 0.239665 + 0.138371i
\(639\) −23.5000 4.48013i −0.929644 0.177231i
\(640\) −3.37014 + 1.94575i −0.133216 + 0.0769125i
\(641\) −16.5805 19.7598i −0.654890 0.780467i 0.331753 0.943366i \(-0.392360\pi\)
−0.986643 + 0.162899i \(0.947915\pi\)
\(642\) 2.12603 11.5875i 0.0839078 0.457322i
\(643\) −10.6331 1.87490i −0.419327 0.0739388i −0.0399966 0.999200i \(-0.512735\pi\)
−0.379331 + 0.925261i \(0.623846\pi\)
\(644\) 4.93198 + 13.2547i 0.194347 + 0.522308i
\(645\) −10.7293 63.4136i −0.422464 2.49691i
\(646\) −33.6927 12.2632i −1.32562 0.482487i
\(647\) 39.5343 1.55425 0.777126 0.629345i \(-0.216677\pi\)
0.777126 + 0.629345i \(0.216677\pi\)
\(648\) 3.31125 8.36873i 0.130078 0.328755i
\(649\) 14.6910i 0.576671i
\(650\) 15.9973 + 5.82254i 0.627466 + 0.228379i
\(651\) −12.7373 + 35.0203i −0.499213 + 1.37255i
\(652\) −12.9374 10.8558i −0.506667 0.425144i
\(653\) 15.9540 + 2.81312i 0.624328 + 0.110086i 0.476858 0.878981i \(-0.341776\pi\)
0.147471 + 0.989066i \(0.452887\pi\)
\(654\) −24.4731 4.49024i −0.956974 0.175582i
\(655\) 66.6108 55.8931i 2.60270 2.18392i
\(656\) 2.11748 + 3.66758i 0.0826736 + 0.143195i
\(657\) 3.30083 3.82492i 0.128778 0.149224i
\(658\) −17.2489 + 10.1239i −0.672433 + 0.394670i
\(659\) 36.4944 6.43494i 1.42162 0.250670i 0.590622 0.806948i \(-0.298882\pi\)
0.830996 + 0.556278i \(0.187771\pi\)
\(660\) −15.9877 9.37871i −0.622320 0.365066i
\(661\) −11.2106 30.8008i −0.436040 1.19801i −0.942047 0.335481i \(-0.891101\pi\)
0.506007 0.862530i \(-0.331121\pi\)
\(662\) 6.88499 + 18.9164i 0.267593 + 0.735205i
\(663\) 0.100050 14.4468i 0.00388563 0.561069i
\(664\) 4.10502 0.723826i 0.159306 0.0280899i
\(665\) 64.0587 37.5979i 2.48409 1.45798i
\(666\) 0.913162 + 0.544215i 0.0353843 + 0.0210879i
\(667\) 6.79368 + 11.7670i 0.263052 + 0.455620i
\(668\) −2.69261 + 2.25937i −0.104180 + 0.0874175i
\(669\) −18.8808 + 22.1874i −0.729974 + 0.857814i
\(670\) 6.02251 + 1.06193i 0.232670 + 0.0410260i
\(671\) −10.8120 9.07233i −0.417392 0.350234i
\(672\) −4.51277 + 0.796789i −0.174084 + 0.0307368i
\(673\) 22.8679 + 8.32324i 0.881493 + 0.320837i 0.742812 0.669500i \(-0.233491\pi\)
0.138681 + 0.990337i \(0.455714\pi\)
\(674\) 22.0079i 0.847712i
\(675\) 8.07241 + 52.0867i 0.310707 + 2.00482i
\(676\) −10.1834 −0.391669
\(677\) 34.4338 + 12.5329i 1.32340 + 0.481678i 0.904546 0.426376i \(-0.140210\pi\)
0.418854 + 0.908054i \(0.362432\pi\)
\(678\) −5.36368 1.99439i −0.205991 0.0765942i
\(679\) 7.91381 + 21.2683i 0.303704 + 0.816203i
\(680\) −19.0471 3.35852i −0.730423 0.128793i
\(681\) 31.2195 11.1187i 1.19633 0.426070i
\(682\) 14.3742 + 17.1305i 0.550417 + 0.655961i
\(683\) 15.9286 9.19636i 0.609490 0.351889i −0.163276 0.986580i \(-0.552206\pi\)
0.772766 + 0.634691i \(0.218873\pi\)
\(684\) 21.3639 3.46265i 0.816869 0.132398i
\(685\) −42.4764 24.5238i −1.62294 0.937005i
\(686\) −18.1657 + 3.60669i −0.693569 + 0.137704i
\(687\) 10.8169 6.14566i 0.412691 0.234471i
\(688\) −8.96644 + 3.26352i −0.341842 + 0.124420i
\(689\) 10.1472 3.69330i 0.386579 0.140703i
\(690\) −17.7981 31.3263i −0.677563 1.19257i
\(691\) 14.3552 2.53121i 0.546098 0.0962918i 0.106209 0.994344i \(-0.466129\pi\)
0.439889 + 0.898052i \(0.355018\pi\)
\(692\) 5.90416 10.2263i 0.224442 0.388746i
\(693\) −13.9180 16.8142i −0.528700 0.638718i
\(694\) −12.1699 21.0789i −0.461963 0.800143i
\(695\) 32.9026 + 39.2118i 1.24807 + 1.48739i
\(696\) −4.14750 + 1.47712i −0.157211 + 0.0559901i
\(697\) −3.65493 + 20.7281i −0.138440 + 0.785135i
\(698\) 13.4592 + 11.2936i 0.509439 + 0.427470i
\(699\) 8.55811 23.0160i 0.323698 0.870546i
\(700\) 20.4350 17.3977i 0.772372 0.657571i
\(701\) 27.2657i 1.02981i −0.857246 0.514906i \(-0.827827\pi\)
0.857246 0.514906i \(-0.172173\pi\)
\(702\) 4.20244 + 7.64117i 0.158611 + 0.288398i
\(703\) 2.55632i 0.0964133i
\(704\) −0.940545 + 2.58413i −0.0354481 + 0.0973929i
\(705\) 39.2580 32.4808i 1.47854 1.22330i
\(706\) 7.71672 9.19643i 0.290423 0.346112i
\(707\) −3.56977 2.95213i −0.134255 0.111026i
\(708\) 7.04686 + 5.99666i 0.264837 + 0.225368i
\(709\) 32.5801 27.3380i 1.22357 1.02670i 0.224943 0.974372i \(-0.427780\pi\)
0.998630 0.0523278i \(-0.0166641\pi\)
\(710\) −15.5162 26.8748i −0.582312 1.00859i
\(711\) −49.8140 0.689996i −1.86817 0.0258769i
\(712\) 4.02974 + 2.32657i 0.151021 + 0.0871920i
\(713\) 7.54808 + 42.8073i 0.282678 + 1.60315i
\(714\) −19.7269 11.3833i −0.738259 0.426009i
\(715\) 16.8769 6.14269i 0.631160 0.229724i
\(716\) 3.80235 + 10.4469i 0.142100 + 0.390418i
\(717\) −8.17520 4.79575i −0.305308 0.179100i
\(718\) −2.68665 15.2368i −0.100265 0.568631i
\(719\) −2.10155 + 3.63999i −0.0783746 + 0.135749i −0.902549 0.430588i \(-0.858306\pi\)
0.824174 + 0.566336i \(0.191640\pi\)
\(720\) 11.0247 3.84059i 0.410866 0.143130i
\(721\) 0.0559211 + 7.81638i 0.00208261 + 0.291097i
\(722\) 21.2410 + 25.3141i 0.790509 + 0.942091i
\(723\) −3.59934 0.660394i −0.133861 0.0245603i
\(724\) 3.68157 + 0.649161i 0.136825 + 0.0241259i
\(725\) 16.5738 19.7519i 0.615537 0.733569i
\(726\) 5.87078 0.993307i 0.217885 0.0368651i
\(727\) 5.68368 15.6158i 0.210796 0.579157i −0.788563 0.614954i \(-0.789175\pi\)
0.999359 + 0.0357966i \(0.0113969\pi\)
\(728\) 2.19258 3.86119i 0.0812623 0.143105i
\(729\) −14.4597 + 22.8017i −0.535543 + 0.844508i
\(730\) 6.55364 0.242561
\(731\) −44.5636 16.2198i −1.64824 0.599912i
\(732\) 8.76507 1.48301i 0.323966 0.0548135i
\(733\) −34.3190 + 40.8998i −1.26760 + 1.51067i −0.506152 + 0.862444i \(0.668933\pi\)
−0.761449 + 0.648224i \(0.775512\pi\)
\(734\) −2.41312 + 13.6855i −0.0890700 + 0.505141i
\(735\) 44.2161 16.4641i 1.63094 0.607286i
\(736\) −4.09479 + 3.43594i −0.150936 + 0.126650i
\(737\) 3.74255 2.16076i 0.137859 0.0795927i
\(738\) −4.17955 11.9977i −0.153851 0.441642i
\(739\) −10.2380 + 17.7327i −0.376609 + 0.652307i −0.990567 0.137033i \(-0.956243\pi\)
0.613957 + 0.789339i \(0.289577\pi\)
\(740\) 0.239448 + 1.35798i 0.00880229 + 0.0499203i
\(741\) −10.6109 + 18.0881i −0.389800 + 0.664483i
\(742\) 2.83609 16.7856i 0.104116 0.616219i
\(743\) −3.65287 10.0362i −0.134011 0.368192i 0.854478 0.519488i \(-0.173877\pi\)
−0.988488 + 0.151296i \(0.951655\pi\)
\(744\) −14.0844 0.0975402i −0.516359 0.00357600i
\(745\) 2.26361 0.399135i 0.0829322 0.0146232i
\(746\) −29.3924 16.9697i −1.07613 0.621304i
\(747\) −12.5038 0.173196i −0.457491 0.00633693i
\(748\) −11.8364 + 6.83374i −0.432781 + 0.249866i
\(749\) 17.6994 3.25162i 0.646723 0.118812i
\(750\) −22.4690 + 26.4040i −0.820453 + 0.964139i
\(751\) −0.707778 + 4.01401i −0.0258272 + 0.146473i −0.994994 0.0999307i \(-0.968138\pi\)
0.969167 + 0.246404i \(0.0792490\pi\)
\(752\) −5.79089 4.85913i −0.211172 0.177194i
\(753\) −0.0238802 + 0.0197576i −0.000870242 + 0.000720009i
\(754\) 1.45905 4.00871i 0.0531356 0.145989i
\(755\) 70.4726 2.56476
\(756\) 13.7465 + 0.187261i 0.499954 + 0.00681061i
\(757\) −29.7948 −1.08291 −0.541456 0.840729i \(-0.682127\pi\)
−0.541456 + 0.840729i \(0.682127\pi\)
\(758\) −2.01256 + 5.52946i −0.0730994 + 0.200839i
\(759\) −23.8641 8.87347i −0.866213 0.322087i
\(760\) 21.5061 + 18.0457i 0.780107 + 0.654587i
\(761\) −1.45761 + 8.26651i −0.0528383 + 0.299661i −0.999762 0.0217963i \(-0.993061\pi\)
0.946924 + 0.321457i \(0.104173\pi\)
\(762\) −7.05056 19.7968i −0.255415 0.717161i
\(763\) −6.86751 37.3817i −0.248621 1.35331i
\(764\) −11.8377 + 6.83448i −0.428272 + 0.247263i
\(765\) 54.2435 + 20.5982i 1.96118 + 0.744730i
\(766\) 19.8041 + 11.4339i 0.715549 + 0.413123i
\(767\) −8.82950 + 1.55688i −0.318815 + 0.0562156i
\(768\) −0.855617 1.50596i −0.0308744 0.0543417i
\(769\) −2.77761 7.63141i −0.100163 0.275196i 0.879482 0.475932i \(-0.157889\pi\)
−0.979645 + 0.200736i \(0.935667\pi\)
\(770\) 4.71698 27.9178i 0.169988 1.00609i
\(771\) 16.9361 + 29.8090i 0.609938 + 1.07355i
\(772\) 1.39067 + 7.88686i 0.0500512 + 0.283854i
\(773\) −26.0125 + 45.0550i −0.935604 + 1.62051i −0.162052 + 0.986782i \(0.551811\pi\)
−0.773553 + 0.633732i \(0.781522\pi\)
\(774\) 28.2569 4.57987i 1.01567 0.164620i
\(775\) 71.4361 41.2437i 2.56606 1.48152i
\(776\) −6.57046 + 5.51327i −0.235866 + 0.197915i
\(777\) −0.281605 + 1.59920i −0.0101025 + 0.0573710i
\(778\) −6.09083 + 34.5428i −0.218367 + 1.23842i
\(779\) 19.6384 23.4041i 0.703619 0.838540i
\(780\) −3.94245 + 10.6028i −0.141163 + 0.379640i
\(781\) −20.6069 7.50028i −0.737371 0.268381i
\(782\) −26.5667 −0.950025
\(783\) 13.0522 2.02284i 0.466449 0.0722904i
\(784\) −3.58638 6.01148i −0.128085 0.214696i
\(785\) −3.08430 + 8.47405i −0.110083 + 0.302452i
\(786\) 24.6713 + 29.8191i 0.879996 + 1.06361i
\(787\) 32.1979 38.3719i 1.14773 1.36781i 0.228761 0.973483i \(-0.426533\pi\)
0.918969 0.394329i \(-0.129023\pi\)
\(788\) −12.0109 2.11785i −0.427871 0.0754452i
\(789\) −11.2271 + 13.1933i −0.399695 + 0.469693i
\(790\) −41.5390 49.5042i −1.47789 1.76128i
\(791\) −0.0625361 8.74099i −0.00222353 0.310794i
\(792\) 4.22351 7.08681i 0.150076 0.251819i
\(793\) −4.30681 + 7.45962i −0.152939 + 0.264899i
\(794\) −1.89672 10.7568i −0.0673120 0.381745i
\(795\) −0.300339 + 43.3678i −0.0106519 + 1.53810i
\(796\) −2.35539 6.47139i −0.0834847 0.229372i
\(797\) −12.2234 + 4.44894i −0.432974 + 0.157589i −0.549307 0.835621i \(-0.685108\pi\)
0.116333 + 0.993210i \(0.462886\pi\)
\(798\) 16.5364 + 28.6268i 0.585384 + 1.01338i
\(799\) −6.52411 37.0001i −0.230807 1.30897i
\(800\) 8.78475 + 5.07188i 0.310588 + 0.179318i
\(801\) −10.5682 9.12020i −0.373411 0.322246i
\(802\) −2.75571 4.77302i −0.0973073 0.168541i
\(803\) 3.54771 2.97688i 0.125196 0.105052i
\(804\) −0.491203 + 2.67720i −0.0173234 + 0.0944175i
\(805\) 35.0737 42.4117i 1.23619 1.49482i
\(806\) 8.77239 10.4545i 0.308994 0.368245i
\(807\) 7.73155 + 45.6961i 0.272163 + 1.60858i
\(808\) 0.598826 1.64526i 0.0210666 0.0578801i
\(809\) 51.6997i 1.81767i 0.417160 + 0.908833i \(0.363026\pi\)
−0.417160 + 0.908833i \(0.636974\pi\)
\(810\) −34.6466 + 5.12410i −1.21736 + 0.180043i
\(811\) 26.0086i 0.913284i 0.889650 + 0.456642i \(0.150948\pi\)
−0.889650 + 0.456642i \(0.849052\pi\)
\(812\) −4.35963 5.12075i −0.152993 0.179703i
\(813\) 45.4647 7.69240i 1.59452 0.269784i
\(814\) 0.746460 + 0.626354i 0.0261634 + 0.0219537i
\(815\) −11.4125 + 64.7233i −0.399761 + 2.26716i
\(816\) 1.55350 8.46704i 0.0543834 0.296406i
\(817\) 44.2478 + 52.7325i 1.54803 + 1.84488i
\(818\) −7.64449 13.2406i −0.267283 0.462948i
\(819\) −8.63063 + 10.1468i −0.301579 + 0.354558i
\(820\) 8.24016 14.2724i 0.287759 0.498413i
\(821\) 35.9281 6.33509i 1.25390 0.221096i 0.493036 0.870009i \(-0.335887\pi\)
0.760863 + 0.648913i \(0.224776\pi\)
\(822\) 11.0459 18.8296i 0.385268 0.656758i
\(823\) −31.1346 + 11.3321i −1.08529 + 0.395011i −0.821872 0.569672i \(-0.807070\pi\)
−0.263413 + 0.964683i \(0.584848\pi\)
\(824\) −2.77622 + 1.01046i −0.0967142 + 0.0352011i
\(825\) −0.334597 + 48.3144i −0.0116492 + 1.68209i
\(826\) −4.73904 + 13.3161i −0.164892 + 0.463325i
\(827\) −34.8967 20.1476i −1.21348 0.700601i −0.249962 0.968256i \(-0.580418\pi\)
−0.963515 + 0.267654i \(0.913752\pi\)
\(828\) 13.9974 7.82494i 0.486443 0.271936i
\(829\) 8.06805 4.65809i 0.280215 0.161782i −0.353306 0.935508i \(-0.614942\pi\)
0.633521 + 0.773726i \(0.281609\pi\)
\(830\) −10.4267 12.4261i −0.361917 0.431316i
\(831\) −20.3419 17.3104i −0.705654 0.600490i
\(832\) 1.65277 + 0.291429i 0.0572997 + 0.0101035i
\(833\) 5.55044 34.3447i 0.192311 1.18997i
\(834\) −17.5536 + 14.5233i −0.607832 + 0.502900i
\(835\) 12.8535 + 4.67830i 0.444814 + 0.161899i
\(836\) 19.8389 0.686143
\(837\) 41.4509 + 8.20026i 1.43275 + 0.283442i
\(838\) 8.30327i 0.286832i
\(839\) −46.5072 16.9273i −1.60561 0.584394i −0.625044 0.780590i \(-0.714919\pi\)
−0.980565 + 0.196196i \(0.937141\pi\)
\(840\) 11.4660 + 13.6583i 0.395615 + 0.471256i
\(841\) 17.2657 + 14.4877i 0.595369 + 0.499574i
\(842\) −19.3340 3.40910i −0.666293 0.117485i
\(843\) −14.6214 41.0545i −0.503589 1.41399i
\(844\) −12.4152 + 10.4176i −0.427349 + 0.358589i
\(845\) 19.8143 + 34.3195i 0.681634 + 1.18063i
\(846\) 14.3354 + 17.5729i 0.492860 + 0.604168i
\(847\) 4.60385 + 7.84396i 0.158190 + 0.269522i
\(848\) 6.33653 1.11730i 0.217597 0.0383683i
\(849\) 18.9240 10.7517i 0.649470 0.368998i
\(850\) 17.2429 + 47.3745i 0.591427 + 1.62493i
\(851\) 0.647820 + 1.77987i 0.0222070 + 0.0610132i
\(852\) 12.0091 6.82303i 0.411426 0.233753i
\(853\) −37.4492 + 6.60330i −1.28224 + 0.226093i −0.772929 0.634492i \(-0.781209\pi\)
−0.509307 + 0.860585i \(0.670098\pi\)
\(854\) 6.87354 + 11.7110i 0.235208 + 0.400743i
\(855\) −53.2384 65.2618i −1.82072 2.23191i
\(856\) 3.40086 + 5.89046i 0.116239 + 0.201332i
\(857\) 26.4169 22.1664i 0.902383 0.757189i −0.0682716 0.997667i \(-0.521748\pi\)
0.970655 + 0.240477i \(0.0773040\pi\)
\(858\) 2.68194 + 7.53042i 0.0915599 + 0.257084i
\(859\) 8.59516 + 1.51556i 0.293263 + 0.0517102i 0.318344 0.947975i \(-0.396873\pi\)
−0.0250811 + 0.999685i \(0.507984\pi\)
\(860\) 28.4449 + 23.8681i 0.969964 + 0.813896i
\(861\) 14.8638 12.4780i 0.506556 0.425248i
\(862\) −14.4373 5.25474i −0.491736 0.178977i
\(863\) 19.9087i 0.677701i −0.940840 0.338850i \(-0.889962\pi\)
0.940840 0.338850i \(-0.110038\pi\)
\(864\) 1.67537 + 4.91865i 0.0569972 + 0.167336i
\(865\) −45.9520 −1.56242
\(866\) −10.0097 3.64324i −0.340144 0.123802i
\(867\) 10.2775 8.50326i 0.349042 0.288786i
\(868\) −7.50295 20.1641i −0.254667 0.684416i
\(869\) −44.9729 7.92993i −1.52560 0.269005i
\(870\) 13.0481 + 11.1035i 0.442372 + 0.376445i
\(871\) −1.69527 2.02035i −0.0574421 0.0684568i
\(872\) 12.4408 7.18271i 0.421299 0.243237i
\(873\) 22.4601 12.5558i 0.760159 0.424950i
\(874\) 33.3963 + 19.2814i 1.12965 + 0.652202i
\(875\) −49.8942 17.7568i −1.68673 0.600290i
\(876\) −0.0202005 + 2.91686i −0.000682510 + 0.0985517i
\(877\) 27.9768 10.1827i 0.944711 0.343847i 0.176686 0.984267i \(-0.443462\pi\)
0.768024 + 0.640421i \(0.221240\pi\)
\(878\) −18.7010 + 6.80660i −0.631127 + 0.229712i
\(879\) −11.6206 + 19.8094i −0.391954 + 0.668156i
\(880\) 10.5389 1.85830i 0.355267 0.0626431i
\(881\) 4.75324 8.23286i 0.160141 0.277372i −0.774778 0.632233i \(-0.782138\pi\)
0.934919 + 0.354861i \(0.115472\pi\)
\(882\) 7.19146 + 19.7303i 0.242149 + 0.664352i
\(883\) 24.7631 + 42.8910i 0.833345 + 1.44340i 0.895371 + 0.445322i \(0.146911\pi\)
−0.0620253 + 0.998075i \(0.519756\pi\)
\(884\) 5.36155 + 6.38964i 0.180328 + 0.214907i
\(885\) 6.49816 35.4169i 0.218433 1.19052i
\(886\) 3.08489 17.4953i 0.103639 0.587765i
\(887\) −28.7681 24.1393i −0.965938 0.810518i 0.0159708 0.999872i \(-0.494916\pi\)
−0.981909 + 0.189354i \(0.939361\pi\)
\(888\) −0.605141 + 0.102387i −0.0203072 + 0.00343587i
\(889\) 24.4423 20.8093i 0.819767 0.697921i
\(890\) 18.1077i 0.606972i
\(891\) −16.4278 + 18.5115i −0.550353 + 0.620158i
\(892\) 16.8203i 0.563184i
\(893\) −18.6523 + 51.2468i −0.624176 + 1.71491i
\(894\) 0.170668 + 1.00871i 0.00570799 + 0.0337362i
\(895\) 27.8090 33.1414i 0.929551 1.10780i
\(896\) 1.68611 2.03888i 0.0563291 0.0681141i
\(897\) −2.80409 + 15.2831i −0.0936257 + 0.510288i
\(898\) 7.21294 6.05238i 0.240699 0.201970i
\(899\) −10.3351 17.9010i −0.344696 0.597030i
\(900\) −23.0385 19.8818i −0.767952 0.662728i
\(901\) 27.6943 + 15.9893i 0.922633 + 0.532682i
\(902\) −2.02231 11.4691i −0.0673354 0.381878i
\(903\) 21.8719 + 37.8632i 0.727850 + 1.26001i
\(904\) 3.10462 1.12999i 0.103258 0.0375829i
\(905\) −4.97566 13.6705i −0.165397 0.454423i
\(906\) −0.217220 + 31.3656i −0.00721664 + 1.04205i
\(907\) −0.149258 0.846482i −0.00495602 0.0281070i 0.982229 0.187684i \(-0.0600981\pi\)
−0.987185 + 0.159577i \(0.948987\pi\)
\(908\) −9.56678 + 16.5702i −0.317485 + 0.549900i
\(909\) −2.68903 + 4.51203i −0.0891894 + 0.149655i
\(910\) −17.2789 + 0.123620i −0.572791 + 0.00409795i
\(911\) 8.53917 + 10.1766i 0.282915 + 0.337165i 0.888722 0.458447i \(-0.151594\pi\)
−0.605807 + 0.795612i \(0.707150\pi\)
\(912\) −8.09800 + 9.51619i −0.268151 + 0.315113i
\(913\) −11.2887 1.99050i −0.373601 0.0658759i
\(914\) 16.7956 20.0162i 0.555548 0.662076i
\(915\) −22.0526 26.6539i −0.729035 0.881152i
\(916\) −2.45664 + 6.74955i −0.0811695 + 0.223011i
\(917\) −29.1922 + 51.4082i −0.964010 + 1.69765i
\(918\) −9.33495 + 24.0789i −0.308099 + 0.794723i
\(919\) −41.8388 −1.38013 −0.690067 0.723746i \(-0.742419\pi\)
−0.690067 + 0.723746i \(0.742419\pi\)
\(920\) 19.5470 + 7.11453i 0.644446 + 0.234559i
\(921\) −10.7168 + 28.8214i −0.353129 + 0.949699i
\(922\) 1.00979 1.20342i 0.0332558 0.0396327i
\(923\) −2.32397 + 13.1799i −0.0764944 + 0.433821i
\(924\) 12.4110 + 2.18546i 0.408292 + 0.0718964i
\(925\) 2.75345 2.31042i 0.0905329 0.0759661i
\(926\) −3.27082 + 1.88841i −0.107486 + 0.0620569i
\(927\) 8.74900 1.41803i 0.287355 0.0465744i
\(928\) 1.27095 2.20134i 0.0417208 0.0722626i
\(929\) −2.46186 13.9619i −0.0807709 0.458075i −0.998189 0.0601508i \(-0.980842\pi\)
0.917418 0.397924i \(-0.130269\pi\)
\(930\) 27.0760 + 47.6562i 0.887857 + 1.56271i
\(931\) −31.9037 + 39.1454i −1.04560 + 1.28294i
\(932\) 4.84889 + 13.3222i 0.158831 + 0.436383i
\(933\) 23.7478 + 41.7982i 0.777468 + 1.36841i
\(934\) −30.6620 + 5.40653i −1.00329 + 0.176907i
\(935\) 46.0612 + 26.5935i 1.50636 + 0.869699i
\(936\) −4.70687 1.78737i −0.153849 0.0584220i
\(937\) −1.73753 + 1.00316i −0.0567625 + 0.0327719i −0.528113 0.849174i \(-0.677100\pi\)
0.471350 + 0.881946i \(0.343767\pi\)
\(938\) −4.08932 + 0.751261i −0.133521 + 0.0245295i
\(939\) −16.3816 45.9968i −0.534595 1.50105i
\(940\) −5.10832 + 28.9707i −0.166615 + 0.944921i
\(941\) 13.0465 + 10.9473i 0.425305 + 0.356873i 0.830177 0.557500i \(-0.188239\pi\)
−0.404872 + 0.914373i \(0.632684\pi\)
\(942\) −3.76208 1.39887i −0.122575 0.0455775i
\(943\) 7.74245 21.2722i 0.252129 0.692718i
\(944\) −5.34223 −0.173875
\(945\) −26.1160 46.6918i −0.849555 1.51888i
\(946\) 26.2399 0.853132
\(947\) 18.0611 49.6224i 0.586906 1.61251i −0.189221 0.981935i \(-0.560596\pi\)
0.776127 0.630577i \(-0.217182\pi\)
\(948\) 22.1611 18.3354i 0.719760 0.595505i
\(949\) −2.16512 1.81675i −0.0702828 0.0589743i
\(950\) 12.7075 72.0676i 0.412285 2.33818i
\(951\) −10.5079 + 12.3482i −0.340743 + 0.400417i
\(952\) 12.9331 2.37597i 0.419163 0.0770057i
\(953\) 27.3754 15.8052i 0.886777 0.511981i 0.0138903 0.999904i \(-0.495578\pi\)
0.872887 + 0.487922i \(0.162245\pi\)
\(954\) −19.3010 0.267347i −0.624893 0.00865568i
\(955\) 46.0662 + 26.5964i 1.49067 + 0.860638i
\(956\) 5.38901 0.950228i 0.174293 0.0307326i
\(957\) 12.1070 + 0.0838455i 0.391362 + 0.00271034i
\(958\) −2.76663 7.60127i −0.0893859 0.245586i
\(959\) 32.8804 + 5.55546i 1.06176 + 0.179395i
\(960\) −3.41048 + 5.81377i −0.110073 + 0.187639i
\(961\) −6.09969 34.5930i −0.196764 1.11590i
\(962\) 0.297342 0.515012i 0.00958670 0.0166047i
\(963\) −6.71273 19.2694i −0.216315 0.620947i
\(964\) 1.82971 1.05638i 0.0589310 0.0340238i
\(965\) 23.8739 20.0326i 0.768528 0.644871i
\(966\) 18.7683 + 15.7412i 0.603860 + 0.506463i
\(967\) −3.82228 + 21.6772i −0.122916 + 0.697093i 0.859607 + 0.510955i \(0.170708\pi\)
−0.982524 + 0.186138i \(0.940403\pi\)
\(968\) −2.20969 + 2.63341i −0.0710222 + 0.0846410i
\(969\) −61.2325 + 10.3602i −1.96707 + 0.332819i
\(970\) 31.3649 + 11.4159i 1.00707 + 0.366543i
\(971\) −23.3166 −0.748265 −0.374133 0.927375i \(-0.622060\pi\)
−0.374133 + 0.927375i \(0.622060\pi\)
\(972\) −2.17382 15.4361i −0.0697253 0.495115i
\(973\) −30.2625 17.1846i −0.970171 0.550912i
\(974\) 6.18117 16.9826i 0.198057 0.544158i
\(975\) 29.0732 4.91904i 0.931087 0.157535i
\(976\) −3.29907 + 3.93168i −0.105601 + 0.125850i
\(977\) −24.2880 4.28263i −0.777041 0.137013i −0.228957 0.973437i \(-0.573532\pi\)
−0.548084 + 0.836423i \(0.684643\pi\)
\(978\) −28.7716 5.27890i −0.920013 0.168801i
\(979\) −8.22511 9.80231i −0.262876 0.313283i
\(980\) −13.2813 + 23.7834i −0.424256 + 0.759733i
\(981\) −40.6975 + 14.1775i −1.29937 + 0.452652i
\(982\) −4.63682 + 8.03121i −0.147967 + 0.256286i
\(983\) 1.76507 + 10.0102i 0.0562969 + 0.319276i 0.999931 0.0117137i \(-0.00372868\pi\)
−0.943634 + 0.330989i \(0.892618\pi\)
\(984\) 6.32688 + 3.71148i 0.201694 + 0.118318i
\(985\) 16.2328 + 44.5992i 0.517220 + 1.42105i
\(986\) 11.8714 4.32085i 0.378064 0.137604i
\(987\) −17.3140 + 30.0047i −0.551112 + 0.955059i
\(988\) −2.10243 11.9235i −0.0668874 0.379337i
\(989\) 44.1716 + 25.5025i 1.40457 + 0.810931i
\(990\) −32.1014 0.444652i −1.02025 0.0141320i
\(991\) 6.38576 + 11.0605i 0.202850 + 0.351347i 0.949446 0.313931i \(-0.101646\pi\)
−0.746595 + 0.665279i \(0.768313\pi\)
\(992\) 6.22935 5.22704i 0.197782 0.165959i
\(993\) 26.5537 + 22.5964i 0.842656 + 0.717075i
\(994\) 16.2588 + 13.4457i 0.515699 + 0.426473i
\(995\) −17.2265 + 20.5297i −0.546116 + 0.650835i
\(996\) 5.56268 4.60238i 0.176260 0.145832i
\(997\) −4.57970 + 12.5826i −0.145041 + 0.398496i −0.990846 0.134995i \(-0.956898\pi\)
0.845806 + 0.533491i \(0.179120\pi\)
\(998\) 25.6434i 0.811728i
\(999\) 1.84083 + 0.0382503i 0.0582412 + 0.00121018i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 378.2.z.a.293.9 yes 144
7.6 odd 2 inner 378.2.z.a.293.4 yes 144
27.20 odd 18 inner 378.2.z.a.209.4 144
189.20 even 18 inner 378.2.z.a.209.9 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.z.a.209.4 144 27.20 odd 18 inner
378.2.z.a.209.9 yes 144 189.20 even 18 inner
378.2.z.a.293.4 yes 144 7.6 odd 2 inner
378.2.z.a.293.9 yes 144 1.1 even 1 trivial